Algebra Examples

${(\sqrt[4]{x})}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{\sqrt[4]{x}}$

Step 2

Multiply $\frac{1}{\sqrt[4]{x}}$ by $\frac{{\sqrt[4]{x}}^{3}}{{\sqrt[4]{x}}^{3}}$ .

$\frac{1}{\sqrt[4]{x}} \cdot \frac{{\sqrt[4]{x}}^{3}}{{\sqrt[4]{x}}^{3}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{1}{\sqrt[4]{x}}$ by $\frac{{\sqrt[4]{x}}^{3}}{{\sqrt[4]{x}}^{3}}$ .

$\frac{{\sqrt[4]{x}}^{3}}{\sqrt[4]{x} {\sqrt[4]{x}}^{3}}$

Step 3.2

Raise $\sqrt[4]{x}$ to the power of $1$ .

$\frac{{\sqrt[4]{x}}^{3}}{{\sqrt[4]{x}}^{1} {\sqrt[4]{x}}^{3}}$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\sqrt[4]{x}}^{3}}{{\sqrt[4]{x}}^{1 + 3}}$

Step 3.4

Add $1$ and $3$ .

$\frac{{\sqrt[4]{x}}^{3}}{{\sqrt[4]{x}}^{4}}$

Step 3.5

Rewrite ${\sqrt[4]{x}}^{4}$ as $x$ .

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Step 3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x}$ as $x^{\frac{1}{4}}$ .

$\frac{{\sqrt[4]{x}}^{3}}{{(x^{\frac{1}{4}})}^{4}}$

Step 3.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{{\sqrt[4]{x}}^{3}}{x^{\frac{1}{4} \cdot 4}}$

Step 3.5.3

Combine $\frac{1}{4}$ and $4$ .

$\frac{{\sqrt[4]{x}}^{3}}{x^{\frac{4}{4}}}$

Step 3.5.4

Cancel the common factor of $4$ .

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Step 3.5.4.1

Cancel the common factor.

$\frac{{\sqrt[4]{x}}^{3}}{x^{\frac{4}{4}}}$

Step 3.5.4.2

Rewrite the expression.

$\frac{{\sqrt[4]{x}}^{3}}{x^{1}}$

Step 3.5.5

Simplify.

$\frac{{\sqrt[4]{x}}^{3}}{x}$

Step 4

Rewrite ${\sqrt[4]{x}}^{3}$ as $\sqrt[4]{x^{3}}$ .

$\frac{\sqrt[4]{x^{3}}}{x}$